The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illustrations, and an Appendix in Five BooksA. & C. Black, 1837 - 390 σελίδες |
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Αποτελέσματα 6 - 10 από τα 33.
Σελίδα 155
... polygons may be divided into the same number of similar triangles : ( 2. ) these triangles have , each to each , the same ratio which the polygons have : and ( 3. ) the polygon AD has to the polygon FK the duplicate ratio of that which ...
... polygons may be divided into the same number of similar triangles : ( 2. ) these triangles have , each to each , the same ratio which the polygons have : and ( 3. ) the polygon AD has to the polygon FK the duplicate ratio of that which ...
Σελίδα 156
... polygon AD to the polygon FK . 3. The triangle ABE has ( VI . 19. ) to FGL , the duplicate ratio of that which the side AB has to the homologous side FG . There- fore , also , ( V. 11. ) the polygon AD has to the polygon FK the ...
... polygon AD to the polygon FK . 3. The triangle ABE has ( VI . 19. ) to FGL , the duplicate ratio of that which the side AB has to the homologous side FG . There- fore , also , ( V. 11. ) the polygon AD has to the polygon FK the ...
Σελίδα 207
... in the same way be demonstrated . If , therefore , & c . This , which is the first proposition of the tenth book , is necessary for some of the propositions of this book . PROP . I. THEOR . SIMILAR polygons inscribed in circles.
... in the same way be demonstrated . If , therefore , & c . This , which is the first proposition of the tenth book , is necessary for some of the propositions of this book . PROP . I. THEOR . SIMILAR polygons inscribed in circles.
Σελίδα 208
... polygon FH . : B E G L M N H K Join BE , AM , GL , FN . Then , because the polygons are similar , and ( VI . 20 ... polygon AC to the polygon FH , is the duplicate of that which BA has to GF . Therefore ( V. 11. ) the square of BM is to ...
... polygon FH . : B E G L M N H K Join BE , AM , GL , FN . Then , because the polygons are similar , and ( VI . 20 ... polygon AC to the polygon FH , is the duplicate of that which BA has to GF . Therefore ( V. 11. ) the square of BM is to ...
Σελίδα 209
... polygon EKFLGMHN : then ( XII . 1. ) as the square of BD is to the square of FH , so is the first of these polygons ... polygon AXBOCPDR to the polygon EKFLGMHN . But the circle AC is greater than the polygon contained in it ; wherefore ...
... polygon EKFLGMHN : then ( XII . 1. ) as the square of BD is to the square of FH , so is the first of these polygons ... polygon AXBOCPDR to the polygon EKFLGMHN . But the circle AC is greater than the polygon contained in it ; wherefore ...
Άλλες εκδόσεις - Προβολή όλων
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 143 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Σελίδα 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Σελίδα 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Σελίδα 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Σελίδα 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 40 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...